Geometry

Question Analysis

This question is about applying the Side - Splitter Theorem. Since in , we can use the proportional relationship of the segments on the sides of the triangle to find the length of .

 

Key Concept Explanation

The Side - Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. In , with , we have the proportion .

 

Step - by - Step Solution

1. We are given that , , and .

2. Substitute these values into the proportion , getting .

3. Cross - multiply:

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